SOME PROPERTIES OF KONHAUSER MATRIX POLYNOMIALS

Abstract

The main aim of this paper is to derive new summation formulas and integral representations for Konhauser matrix polynomials. In addition, we obtain a raising operator and a Rodrigues formula for these matrix polynomials.

Keywords

• Laguerre matrix polynomials,Konhauser matrix polynomials,Raising operator,Rodrigues formula

References

1. : J. D. E. Konhauser, Biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math. 21 (1967) 303-314.
2. : L. Spencer, U. Fano, Penetration and diffusion of X-rays. Calculation of spatial distribution by polynomial expansion, J. Res. Nat. Bur. Standards 46 (1951) 446-461.
3. : E. Defez, L. Jódar, A. Law, Jacobi matrix differential equation, polynomial solutions and their properties, Comput. Math. Appl. 48 (2004) 789-803.
4. : E. Defez, L. Jódar, Some applications of the Hermite matrix polynomials series expansions, J. Comp. Appl. Math. 99 (1998) 105--117.
5. : E. Defez, L. Jódar, Chebyshev matrix polynomials and second order matrix differential equations, Util. Math. 61 (2002) 107--123.
6. : L. Jódar, R. Company, Hermite matrix polynomials and second order matrix differential equations, Approx. Theory Appl. 12(2) (1996) 20--30.
7. : L. Jódar, R. Company, E. Navarro, Laguerre matrix polynomials and system of second-order differential equations, Appl. Num. Math. 15 (1994) 53--63.
8. : L. Jódar, R. Company, E. Ponsoda, Orthogonal matrix polynomials and systems of second order differential equations, Differ. Equ. Dyn. Syst. 3 (1996) 269-288.

9. : L. Jódar, E. Defez, E. Ponsoda, Orthogonal matrix polynomials with respect to linear matrix moment functionals: Theory and applications, J. Approx. Theory Appl. 12(1) (1996) 96--115.
10. : K. A. M. Sayyed, M. S. Metwally, R. S. Batahan, Gegenbauer matrix polynomials and second order matrix differential equations, Divulg. Mat. 12(2) (2004) 101-115.
11. : S. Varma, B. Çekim, F. Taşdelen, On Konhauser matrix polynomials, Ars Combin. 100 (2011) 193-204.
12. : S. Varma, F. Taşdelen, Biorthogonal matrix polynomials related to Jacobi matrix polynomials, Comput. Math. Appl. 62(10) (2011) 3663-3668.
13. : N. Dunford, J. Schwartz, Linear Operators. Vol. I, Interscience, New York, 1957.
14. : L. Jódar, J. C. Cortés, On the hypergeometric matrix function, J. Comput. Appl. Math. 99 (1998) 205-217.
15. : B. Çekim, A. Altın, R. Aktaş, Some relations satisfied by orthogonal matrix polynomials, Hacet. J. Math. Stat. 40(2) (2011) 241--253.